We report a λ. ≲ 1 cm search for rotational molecular absorption towards quasars, now possible with the upgraded Australia Telescope Compact Array (ATCA). The targets were PKS 0201+113, PKS 0336-017 and Q 0537-286, where known damped Lyman-alpha absorption systems (DLAs) could cause redshifted molecular absorption in the 12-mm band of the telescope. We place 3σ upper limits on any HCO+ 0 → 1 absorption features of <30 mJy per 3.4 km s-1 channel. The non-detections could be attributed to the inherent low metallicities in DLAs leading to generally low H2, and thus HCO+, column densities. In general, the detection of molecular rotational transitions in DLAs could be further hindered by a lower than expected CO-to-H2 conversion ratio, whether due either to photoionization of carbon or to its relative under-abundance at high redshift.